A185786 Third accumulation array of A107985, by antidiagonals.

1, 6, 6, 21, 35, 21, 56, 120, 120, 56, 126, 315, 405, 315, 126, 252, 700, 1050, 1050, 700, 252, 462, 1386, 2310, 2695, 2310, 1386, 462, 792, 2520, 4536, 5880, 5880, 4536, 2520, 792, 1287, 4290, 8190, 11466, 12740, 11466, 8190, 4290, 1287, 2002, 6930, 13860, 20580, 24696, 24696, 20580, 13860, 6930, 2002, 3003, 10725, 22275, 34650

Offset: 1

Author

Clark Kimberling, Feb 03 2011

Keywords

• nonn
• tabl

Comments

See A185784. The pattern established by the formulas for A185785, A185786, A185787, suggests that the H-th accumulation array of A107985 may be given by

T(n,k)=(n+k+H)C(n+H,H+1)C(k+H,H+1)/(H+2).

Examples

			Northwest corner:
1....6.....21.....56.....126
6....35....120....315....700
21...120...405....1050...2310
56...315...1050...2695...5880
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A185784.

Programs

Mathematica

(See A185784.)
f[n_, k_] := Binomial[k + 3, 4]*Binomial[n + 3, 4]*(n + k + 3)/5; Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 12 2017 *)

Formula

T(n,k) = (n+k+3)*C(n+3,4)*C(k+3,4)/5.